Plasmon emission by electrons in reflection high energy electron diffraction

The theory of plasmon emission by fast electrons moving into or reflected from a dielectric is extended to the case where both the electron and the plasmons are treated quantum mechanically. This is necessary to allow consideration of experiments where the electron is diffracted, as is particularly the case for reflection high energy electron diffraction. The theory presented here is based on treating the dielectric medium as uniform, which allows an approximate quantisation of the plasmons and hence leads to a result which permits ready numerical evaluation. The commonly-used semi-classical treatment of the problem is critically analysed to allow the advantages of the current approach to be demonstrated. Examples are given to demonstrate the applicability of the new theory. In particular, it is shown for a one-dimensional model of a surface how the plasmon emission depends on the Bloch wavefunctions of the crystal and that the emission is strongly influenced by the amount of absorption due to inelastic scattering in the dielectric medium.